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A360108
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Sum of squares of digits of primorial base expansion of n.
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1
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0, 1, 1, 2, 4, 5, 1, 2, 2, 3, 5, 6, 4, 5, 5, 6, 8, 9, 9, 10, 10, 11, 13, 14, 16, 17, 17, 18, 20, 21, 1, 2, 2, 3, 5, 6, 2, 3, 3, 4, 6, 7, 5, 6, 6, 7, 9, 10, 10, 11, 11, 12, 14, 15, 17, 18, 18, 19, 21, 22, 4, 5, 5, 6, 8, 9, 5, 6, 6, 7, 9, 10, 8, 9, 9, 10, 12, 13, 13, 14, 14, 15, 17, 18, 20, 21, 21, 22
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OFFSET
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0,4
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LINKS
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FORMULA
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For all n >= 0, a(2n+1) = 1 + a(2n).
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EXAMPLE
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5 in primorial base (A049345) is written as "21" (because 5 = 2*2 + 1*1), therefore a(5) = 2^2 + 1^2 = 5.
23 in primorial base is written as "321" (because 23 = 3*6 + 2*2 + 1*1), therefore a(23) = 3^2 + 2^2 + 1^2 = 14.
24 in primorial base is written as "400" (because 24 = 4*6 + 0*2 + 0*1), therefore a(24) = 4^2 = 16.
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MATHEMATICA
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a[n_] := Module[{k = n, p = 2, s = 0, r}, While[{k, r} = QuotientRemainder[k, p]; k != 0 || r != 0, s += r^2; p = NextPrime[p]]; s]; Array[a, 100, 0] (* Amiram Eldar, Mar 06 2024 *)
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PROG
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(PARI) A360108(n) = { my(s=0, p=2, d); while(n, d = (n%p); s += d^2; n = (n-d)/p; p = nextprime(1+p)); (s); };
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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